Question

The volume of a cylinder is 32.25 cubic inches. If a cone has the same height and radius as the cylinder what is its volume?

Answer 1

Cylinder volume is Pi*r^2*h
Cone is 1/3 the volume of a Cylinder.
32.25/3 = 10.75

Answer 2

10.75 cubic inches

Explanation:

Hello, I can help you with this

we need to remember the formula for the volume of a cylinder

Volume of a cilynder

V=
`area*heigh\\\pi *radius^(2)*height \\`

now the volume of a cone is given by:

`(1)/(3)*area*heigh\\(1)/(3) * \pi *radius^(2)*height \\\\`

if the cone and the cylinder have the same radius and height

Volume of the cylinder= 32.25 cubic inches=
`\pi r^(2)*h\\`

now, we know

`32.25\ cubic\ inches =\pi r^(2)*h\\\\`

replace this value into the volume of the cone

volume of the cone=

`V=(1)/(3)*\pi r^(2)*h \\V=(1)/(3) *32.25\\V=10.75`

so, the volume of the cone is 10.75 cubic inches

Have a nice day